Solve for $x$ and $y$ using elimination. ${-2x+y = -2}$ ${-5x-3y = -49}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $3$ ${-6x+3y = -6}$ $-5x-3y = -49$ Add the top and bottom equations together. $-11x = -55$ $\dfrac{-11x}{{-11}} = \dfrac{-55}{{-11}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {-2x+y = -2}\thinspace$ to find $y$ ${-2}{(5)}{ + y = -2}$ $-10+y = -2$ $-10{+10} + y = -2{+10}$ ${y = 8}$ You can also plug ${x = 5}$ into $\thinspace {-5x-3y = -49}\thinspace$ and get the same answer for $y$ : ${-5}{(5)}{ - 3y = -49}$ ${y = 8}$